Method of determining the elasticity of porous packing structures



April 21, 1936..

H. T. WHEELER METHOD OF DETERMINING THE ELASTICITY OF POROUS PACKING STRUCTURES e'et l 8 4 Sheet INVENTOR April 21, 1936; H. T. WHEELER 2,038,091 METHOD OF DETERMINING THE ELASTICITY OF POROUS PACKING STRUCTURES Filed May 15/1951 4 Sheet eet 2= 7 I6 IN VEN TOR.

April 21, 1936.

H. T. WHEELER METHOD OF DETERMINING THE ELASTICITY OF POROUS PACKING STRUCTURES Filed-May 15, 1931 4 Sheets-Sheet 5 P7 P8 f? INVENTOR.

H. T. WHEELER 2,038,091 METHOD OF DETERMINING THE ELASTICITY OF POROUS PACKING STRUCTURES April 21, 1936.

-Filed May 15, 1931. 4 Sheets-Sheet 4 INVENTORQ Patented Apr. 21, 1936 I PATENT OFFICE METHOD OF DETEKMINING THE ELAS- TICITY F POROUS PACKING STRUC- TURES Harley T. Wheeler, Dallas, Tex. Application May 15, 1931, Serial No. 537,658

1 Claim. (CI. 73-51) This invention relates to a method of determining the elasticity of porous elastic structures under the tension of pressure while in contact The term pressure will be used throughout .the description as indicating fluid pressure as applied to the packing.

15 Still another advantage is that the friction due to permanent deformation of the elastic structure may be obtained.

One other advantage is that the correction may be obtained which is necessary to determine the 20 volume of fluid required to compensate for saturation of the porous structure under pressure.

Another advantage is that the fatigue point of the elastic structure may be obtained.

Yet another advantage is that the relation of 25 the deformation due to rigor may be obtained.

Still another andimportant advantage isthe capability of ascertaining by means of friction the internal-pressure saturation resulting from repeated applications of pressure.

30 With the foregoing objects and advantages in view, other desirable features of testing will be shown during the description, accompanied by the drawings, wherein:

Figure 1 is a cross-sectional View of a testing 35 machine in which samples of elastic porous structures, such as rod-packing, may be inserted for examination.

Figure 2 is an end view of the testing machine, of Figure 1. 1 4,0 Figure-3 is an elevational view of the testing machine arranged for testingbearing load on the.

packing.

Figure ,4 is a vertical external view of the testing machine arranged to test packing for vibra- 45 tion.

Figure 5 is a set of graphic curves depicting the rise of friction due to variation of pressure which is applied per unit of time.

Figure 6 is a set of internal-pressure curves of 50 a packing denoting the effect of varying the time of application of pressure.

Figure '7 is a fluxion curve of a rod-packing showing the effect on internal-pressure of reducing the pressure impressed.

55 Figure 8 is a fluxion curve of the successive starting and stopping of the rod during the rise and fall of pressure, at a certain rate of time between applications of pressure.

Figure'9 shows the representative fluxion curves of a packing not saturated and saturated, due to repeated impressions of pressure.

Fig. 10 shows the maximum and minimum curve where'pressure is applied intermittently.

Figure 11 is the fluxion curve of a liquid seal packing which is due to rigor, a temporary 1o deforming of the structure which traps the fluid under pressure.

Figure 12 is the maximum and minimum curves of a packing under rigor of deformation, at a certain rate of intermittent applications of pressure.

Figure 13 is the fluxion curve of a packing at the fatigue point, or permanent deformation.

Figure 14 is the maximum and minimum curves of a packing approaching the fatigue point, while intermittently impressed with pressure.

Referring now especially to Figure 1, the main frame I of the testing machine contains the stufling-boxes, the partition la dividing them.

' The partition la has a clearance to admit the shaft 4, without contact. The packing glands 2 and 3 adjust the packing in the two stuffingboxes and are adjusted by the cap screws 24, 24,

shown in the end view, Figure 2. Returning now to Figure 1, the rod 4 is threaded internally on both ends at 5a and 6, so that an eye-bolt 5 may be attached. The pulley I is seated on the rod 4 by means of a hexagon shape 4a. The flexible rope 8 is attached to the pulley I and is used to rotate the rod assembly.

As shown 'in Figure 2, the rope 8 is attached to the rim of the pulley 1 and is held in place by a clamp 25. This view also indicates the hexagon fit 4a on the end of the rod 4, fixing the pulley 'to the latter. The threaded hole 6 admits an 40 eye-bolt for translation tests. The packing gland 2 is held and adjusted by the cap screws 24, 24-. To rotate the rod 4 and measure the friction, a rope 8 is attached to the draw-bar 30 of the spring balance 26. The spring 30a is attached to the inside of the frame 26 and is compressed by a pull on the draw-bar 30. To the draw-bar 30 is attached a pointer 21 to indicate the pull on the spring 30a by means of a calibrated scale 28. The rope 29 is attached to the frame 26 and is connected to the source of movement.

' Referring again to Figure 1, the partition Ia has a passage 9a into the clearance around the rod 4, the outer entranceof 9a being threaded to hold a piping assembly 9 to admit a fluid under pressure from a suitable source. The passage Ilia to the clearance around the rod 4 is threaded at its outer entrance to hold a valve body III. The passage Illa is extended thru the body III by a passage l I a, a needle valve ll being used to open 'or close the latter. A plurality of packing rings 1), 9,1) in one stufiing-box are alike and equal in number to the rings 1', r, r in the adjacent box, both sets being fitted and adjusted to suit the conditions under examination.

The samplingpipes I2, l2, etc., are pushed into I slightly tapering sockets in the frame I, the inside ends of the pipes being positioned to measure internal pressures in the packing'or pressures of the surface adjacent to the packing. To the outer end of each pipe i2 is attached a visible dial gauge for measuring pressure. The gauges l3, l4 and I5 and the connected pipes l2, are positioned to measure the pressure of the stufllngbox wall, at the center of the rim of each packing ring a", r, r. The gauges l6, l1 and la'and the connecting pipes I2, are positioned to measure pressure existing at the geometrical center of each annular packing ring p, p, p. The gauges I 9 and 20 and the connecting pipes l2 are positioned to measure the pressure existing between the joints of the packing rings 1), p, D. The gauges 2|, 22, 23 and the connecting pipes l2 are positioned to measure the pressure of the fllm existing onthe rod surface, in the middle of each packing ring, r, r, r. The foregoing are but examples of the method of investigating the internal pressures of packing by sampling tubes directed to the desired points. Any kind of packing may be so investigated.

The testing machine shown in Figure 3 is an elevation-of the cross-sectional view of Figure 1. The packing to be tested is held around the rod 4 and inside the main frame I, by the glands 2 possible by the addition of the weights G, G placed and 3 and adjusted by the cap screws 24, 24. The rod 4 is threaded internally at both ends at 5a and 6 to admit an eye-bolt so that the shaft 4 may be translated in either direction. A pulley I is flxed to the shaft 4 so that a pull of the rope 8 will rotate the shaft 4 in either direction. The gauges I2 to 23 inclusive, attached to the sampling pipes l2, the latter positioned at required points in the packing assembly as demonstrated in Figure 1, will indicate the variation of internal pressure. Fluid pressure is applied to the packing thru a pipe 9 and exhausted thru the valve l0 s by means of the needle valve II. The machine described up to this point will indicate the friction .due to the pressure impressed on the packing, plus whatever effect the moving parts have, to wit, theshaft 4, the eye-bolt 5 and the pulley 75. As the latter three parts are slight in weight by proportion to the'eifect of the applied pressure thru the-piping 9, investigation of weight or bearing thrust against the packing is made on the standards 3| and 32. The downward pull of the weights G, G is transferred thru the bearing balls 35, 35 to the collars 33 and 34. The ball bearing suspension eliminates any torsional efl'ect,on the shaft 4 during rotation and maintains the weight in one position, the vertical.

Inasmuch as a bearing thrust is a dead weight in a given direction, it is desirable in some cases to investigate the friction of packing, .devoid of all side thrusts. .In Figure 4 is shown the testing machine, the rod 4 in a vertical position. The friction of the packing against therod 4 will hold the latter in any position and its weight is so slight in comparison to the friction that no thrust taking surfaces are needed to locate the shaft in an endwise position. The rod 4 may be rotated by a pull on the rope 8 thru the pulley I. Likewise the rod 4 may be translated in either direction by connecting the spring balance 26, of Figure 2, to the eye-bolt 5. The packing samples are placed around the rod 4 and inside the main frame I in the stufling-boxes provided and held by the glands-2 and 3, and adjusted by the cap screws 24, 24. .Thegauges l3 to 23 inclusive being attached to the pipes l2, the latter being positioned in the annular packing ring sections so that the internal pressure may be measured. Pressure is applied to the packing thru a pipe 9 and is exhausted thru a valve ll.

" The matter of vibration, of high or low pitch,

is a bearing load of short duration of time. In Figure 4 is shown an arrangement for producing vibration in the rod 4 by a convenient means. The assembly S is a solenoid composed of a coil of wire of tums 3| and with an iron core 36, which by position of the assembly S may be made to vibrate against the rod 4 by connecting the terminals 38 and 39 to a source of intermittent electric current. Arrangements are made at the source of current to vary the period of current reversals, the positionof the assembly S with respect to the rod 4 varying the intensity of thrust.

The operation of testing packing with this machine is to insert the samples in the two- Figurej-l, and as the particular test may demand' A fluid medium under pressure is admitted thru the pipe assembly 9 and is confined to the machine by closing the needle valve l l' in the valve body H). The pressure indicated by the gauges l3 to 23 inclusive are recorded with the shaft :4 in a condition of motion or of rest. To secure the friction of movement, a-pull is made on the rope 29 of Figure 2 and the rate of movement obtained by an instrument such as atachometer. The spring 39a is compressed and the pointer 21 will indicate on the scale 28, a certain pull as the pulley I begins to move. The shaft 4 and the pulley 1 may be rotated at any rate of speed, stopped, started and may be oscillated by alternately reversingthe direction of pull. When referred to the particular movement of the shaft the pull indicated by the springscale 28, together with the pressures indicated by the gauges l3 to gauges I9 to 23 will rise, while those indicated by the gauges l3 to I8 inclusive will fall. The pull indicated by thescale 28, of Figure 2, may or may not show a difference with the'addition of the weights, G, G. If sufllcient weights G, G are added the packing rings will be deformed the pressure will finally escape along the rod 4. The foregoing conditions and similar changes in physical properties of the packing. when' re- 25.. flow of seepage thru the packing, as is shown in ferred to the amount of the weights, G, G, the speed of rotation of the shaft 4 and the pull sho wn by the scale 28, are the determining factors of the .characteristics of the packing, as it is tested.

In testing packing for reaction to vibration, it is desirable to eliminate all dead weight thrust, soles in Figure 4, the rod 4 is placed in a vertical position. The pull-for rotation is secured by the rope-8 and recorded in amount from the readings of the pointer Z'l on the scale 28, as shown in Figure 2. The solenoid S is actuated by an intermittent electric current to adesired pitch. and the position of the same solenoid S with respect to the rod 6 determines the thrust of the plunger 36. The pressures of the gauges i3 to 23 inclusive, together with the .pull' registered on the scale 28, as referred to motion and rate of movement of the shaft 4, are determining factors of the packing characteristics under the existing physical conditions.

While testing packing for elastic recovery during the impression of pressure, bearing load, vibration and similar influences, a meter M is installed in the piping assembly 9 to measure the Figures 1, 3 and 4.

While the foregoing methods of testing packing have been chiefiy' described as a means of determining the characteristics of rotation, it

should be evident that oscillation and translaly indicate the internal pressures and the f'ric-' tion reactions in character with the changes of physical properties and the accompanying conditions.

The present invention relates to the method of determining the rate of internal flow of a pressure fluid confined within a porous structure 'which causes theincrease or decrease'of friction by a corresponding variation of the volume of the porous structure due to the impressing and releasing of pressure, and is one of a group of separate inventions which may be practiced and which are disclosed in my cope'nding applications:

Serial No. 526,287 filed March 30, 1931, which relates to a machine for taking reactions of porous or elastic bodies under confinement and subjected to fluid Pressure;

Serial No. 526,288, filed March 30, 1931, which relates to a method of determining the dropof pressure which occurs in a porous or elastic body under confinement and subjected to fluid pressure and the friction which is caused by the thrust due to the drop in pressure;

Serial No. 533,430, filed April 28, 1931, which relates to the method of determining the inter- .The first two laws of friction are disclosed in my application Serial No. 526,288, while laws 3, 4 and 5 will be found in my application Serial No. 533,430.-

In thepresent invention, the total amount of energy consumed in the form of friction by repeated applications of pressure is investigated, each application of pressure being considered a cycle of pressure events, solved for any instant by the first and second laws, and for the cycle by the third, fourth and fifth laws. For any considerable length of time during whichthere are many. pressure applications, a new set of relations is necessary which take into account the energy consumed, the temperature developed and the volume of seepage flow. The chief result of this investigation will be represented by a discrimination between the true coefiicient of fric- 1 tion and the effective value. The true coefiicient will be shown to be that value for any instant as determined by the first and second lawsfcr the contact occuring on an increment of surface. The eifective ccefficient will be shown to be based on the consumption of energy toovercome an average of friction conditions. But the fluxion values of repeated impressions of pressure can only be determined thru the volume and pressure relations which are regulated by the porosity existing and which may be expressed as a measure ofelasticity, or a capability of resuming an original position afteran impression of pressure.

Porosity is defined as a state of being porous, and inthis investigation refers to the structure of the packing as it is inserted in a testing machine or an actual stuifing-box in operation. Referring now to Figure 5, a chart having ordinates expressed in friction, f0, 1, 7" and. f", and abcissa of impressed pressure OPhand OP, it is to be supposed that a material of the greatest pessible porosity, having no resistance to the how of pressure, is tested in the machine of Figure 1, and that the friction of rotation at zero pressure is fol If there is no resistance to flow, then there will be no increase of friction due to-the rise of pressure, as with line JOO. And in Figure 6, an internal pressure diagram of the relations of Figure 5 the ordinates being made to impressed pressure and the abcissa being the length of the packing set, the pressure P would be decreased from point (1 to' point e in an infinitesimal length of the contact surface during a fractional length of time to .flow out of the box without change of internal pressure, along the line'eg, or line 0.

The hypothesis is untenable; if thereis a com Figure 6, the pressure P drops from point d to point a, or zero. 'I'herebeing a drop of pressure during the flow thru the packing, there will be an increase of friction, as line fol, of Figure 5. As

the density of the packing is increased, its porosity decreases due to the refinement of the passages and pores, as forexample the curves 2, 3 and t of Figure 6 representing a single structure of a given initial porosity, give differentiriction increases of foj2, fof'3 and fof'fl respectively,'ac-

65 Y the material under pressure along the rod surcordingto diflzerent rates of pressure application, line I04 being the sfowest and line I02 being the fastest. It may be'noted that the curves. 2 and 3, of Figure 6,. approach the maximum length of the set at point g, at'points b and 0. respectively, the rise of impressed pressure causing a reaction of the structure, decreasing the porosity and confining the pressure. The curves 2, 3' and. 4' represent the rates of time of application, a very'qguick application of pressure giving curve 2, and a. very slow one the curve 4. Curve 4 of Figure 6 is. the

maximum internal pressure relation than can be obtained from pressure P of Figure by delaying the time of application, that is, for a slow application no more friction than fof'k can be obtained. This is the point of saturation, which has been expressed in the fourth law-of friction, but in this case bringing in the degree. of porosity;

It is now necessary to more specifically account for the tendency of an elastic. structure to occupy a larger volume during the impression of pressure and this is done by the additional terms of the volume of. occupancy V which the packing is adjusted to, and-the volume S of the seepage per unit of time which is measured by the meter M of the Figures 1, 3 and14.

The degree of porosity is defined as. unity when .thereis no restriction'to flow thru thestuflingbox of Figure 1, the condition being that of. an orifice discharging into the air. The porosity is further defined as being zero when there is noflow thru the structure, being equivalent to replacing the packing gland with a tight partition from the rod to the wall. Between the degrees I of unity and zero is an infinite series of values lower than at points of lower porosity andhigher:

density. A r elation can then be established that the internal pressure of any one increment of the pacln'ng volume, times thevolume S of the seepage flow thru that increment of volume can be madeequal to the same relation of any other increment of packing volume, by controllingtheporosity by means of the density of the structure.

Returning again to Figure 5, on the abcissa of impressed pressures are further plotted the ordinatesof seepage flow per unit of time, as

measured'by the meter M of Figures 1, 3 and 4.

- It has been found that the rate of seepage flow is highest with the fastest application of pres.-

sure', slowing down in rate'as the length of time of application increases. As specially referred ,..to the friction of movementis obtained by the internal pressure measurements taken on therod surface. A quick impression of pressure forces face .toform a film between the structure and the solid body before the pores of the structure have had' time to absorb the pressure and react, giving a low friction value. A slow application of impressed pressure shows a slow rate of seepage flow, the structure having sufficient time to. absorb and react against the rod, to close up the pores, excluding most of the pressure adjac'ent tothe rod surface by increasing the densiaosaoar ty and directing'the fiow toward the. stuflingbox walls- This is reflected-in the seepage lines 2s, 3s" and 4:, corresponding to the frictionlines 2, 3 and 4' of Figure '5.

The tendency of a porous elastic ring in fluid tension to contract toward the smallest diameter where the seepage is excluded on the rod surface, and particularly on rotating shafts is a factor of curvature not herein considered. But at this point this action does point to the question',v as to whether the-packing should be fixed to: the. shaft so that the better circulation of seepage could be utilized at the outside contact, thus avoiding the lower porosities due to' reaction, and the consequent increase of friction'. The

a porous elastic structure is applicable for increase or decrease of impressedpressure, as reaction is basically afiected by the element'of time included in: the rate of flow. From the relation established between the friction and the rate of fl'ow'of seepage' a relation is stated:

The flow of seepage on the surface of a solid body in contact with a porous elastic structure in reaction due to impressed pressure, is inversely proportional to the length of ,time of pressure ing a higher actual contact per unit of area upv to the. point at which there are no voids, when friction becomes constant for a given impressed pressure. Hence to the five laws developed in the companion applications above identified flow of seepagein its effect on the reactions of may be added the sixth law of friction of an elasv tic body in contact with a solid moving body:

6. For a constant pressure, friction is inverse- Iy proportional to the degree of porosity and becomes constant at the zero value.

The seventh law follows from the sixth:

7. Friction is inversely proportional to the rate of seepage flow at the surface of contact between a solid moving body and a porous elastic structure reacting. under pressure, up to the point of saturation.

Returning 'now to the consideration of the tendency of a porous elastic structure to occupy. a. larger volume during the impression of pressure, which-previously has been referred to as the relation of the internal pressure and the rate of seepage flow per unit of time. Experiment, as well as practice, demonstrates that after pressure has been impressed on a set of packing, that the packing creates a greater friction afterward, for anappreciable time, and .that this excess friction may be reduced by loosening the packing gland to increase the volume of occupancy. This may be done up to a certain pointfwhen the pressure will cut a lane thru the structure and escape.

Referring now to Figure '7, a. fluxion chart ofa set of porous elastic packing in contact with the rod of Figure 1, the ordinates being friction otmovement and plotted to a unit of measurement, the abcissa being impressed pressures to a unit of measurement starting with P0, and increased by P1, P2, P3 and P. At the latter points of pressure are shown the internal pressure charts 7a, 7b; 7c, 7d and 7e respectively, the ordinates being impressed pressures P0, P1, P2, P3 and P respectively, the "abcissa of every chart being the length of the packing set. The fricpressed pressure.

tion due to the rise of normal applied pressure is represented by the line Q, that due to the reduction of pressure by curve R. The curves Q and R are the internal pressures for the length 'of the packing at theqespective points of im- The friction fa is due, to the initial-set of tightening the packing, and the line Q increases proportionally to. the impressed pressure, giving the friction F at the pressure P. The pressure is then reduced at such a rate that the pressure trapped internally does not have time 'to drain out of the structure, giving the curve R of higher friction than line Q, that is, the reaction is reflux. At pressure P, the internal pressure curves Q, and R are coincident giving equal friction and a unity fluxion value. At pressure Pa, the residual maximum pressure in the structure is P3, less than P and greater than P3, and R is greater than Q by the means of averaged internal pressures. curve R is greater than that of Q, hence a higher friction is secured with the reduction of 'pressure.

At pressure P2 the residual maximum pressure is P2, less than P3 and greaterthan ,Pz, giving a higher friction dueto the higher mean of.

y by increasing the volume of occupancy, and

that when this is done the measured seepage flow increases. At point a: for; example, it has been found that the ,mean'effective value of the curve R times the volume of seepage flow per unit of time, is equal to the mean effective value of curve Q times the seepage flow per unit of time at the point 11 of friction. This leads to the eighth law of friction due to contact between a porous elastic structureand a solid moving body: 8. The value obtained by multiplying the mean eifective inte nal pressure and the seep'age flow per unit of time is equal for any friction obtainedat any given impressed pressure. v

Thus by taking the required measurements of seepage flow, the friction per unit of area contact, the volume of occupancy of the structure,

and the internal pressures, the degreeof porosity and the true coeflicient of frictioh for any increment of surface can be obtained, as well as the effective value of friction. 'Since the volume of occupancy varies .the friction of contact, the change of volume may be expressed in terms of friction and the volume of the seepage flow. Ifthe structure is in reflux, it creates a higher friction during the reduction of pressure; for example at a given impressed pressure'when. the volume is increased to reduce the friction, the rate of seepage flow will rise. Then if the structure is in flux, and the volume is decreased to raise the friction, the seepage flow decreases or may return seepage to the source of pressure. The followingrelations are the ninth and tenth laws of friction and independent of the speed of movement:

9. The additional volume of occupancy needed to decrease the friction of contact between a The mean' pressure drop of porous elastic structure and a solid moving body I have found that vibration against packing causes a hydraulic action in the pores and in- 1 terstices which induces a higher internal pressure than the structure would experience from the impressed pressure. This action is a form of saturation caused by movement of the solid body and is measurable by the eleventh law:

'11. The value of the reaction which a porous elastic structure'expends against a vibrating solid body is equal to the energy exhausted by the flow of seepage.

, Should it be desirable to ascertain the reaction 7 caused by vibration in addition to normal pressure impressed, the total energy exhausted by seepage is credited with the amount used under normal operation and pressure only. The duty imposed by vibration and misalignment is varied and any of the manifestations of internal pressure, seepage flow, the volume of occupancy, and the like may be equatedto the quantities desired. This subject matter is disclosed in my applicatio Serial 526,288 previouslycited.

@I'he most important means of obtaining the actual performance of an elastic structure in contactwith a solid moving body are the elasticity relations, including the work of deformation.

These are time- -friction relations which obtain while the structure is reacting during the applications of pressure. It should be apparent porosity and the tendency of the structure to become saturated with the material under pressure. Referring now to Figure '7, the coefficient of elasticity is defined as the relation of stress to strain, the impressed pressure being considered a force or stress, and the friction a reaction, or a strain. The line Fow is the line of initial-set, the ordinatesfrom this line to the friction line Q being the actual increase of friction due to the increase of pressure. If for any point on the line Q, the impressed pressure is divided by the actual friction due to the pressure, a constant ratio is obtained, the constancy of this ratio being uniformly characteristic for all types of packing and other porous elastic structures differing only in the value of the'co-' eflicient, that is, the slope of line Q. The ratios obtained from the line R, the friction due to the reduction of pressure, the actual ordinates of friction being taken from the line Fo'v, are not constant for any impressed pressure, nor for any type of packing or similar elastic porous structure. As the coefficient of elasticity varies with the type of packing, it is the ideal comparison. The twelfth law of friction may thenbe stated 12. The coefiicient of elasticity of a porous elastic structure in contact with a solid moving body is the ratio of the imrpress'ed pressure to the actual friction of contact caused by that pressure, and is constant for the rise of pressure only. For any cycle of pressure events in reflux, the fluxion curve. will give the hysteresis value as a direct reading in friction, as shown by Figure '7,

'that elasticity is linked with the density,'the

being F0 F0. If n seconds are required for the value F0 F0 to reduce to F0, then the elastic recovery will be the value F0 F0 divided by n, or a rate of friction decrease per unit of time. Thus after a structure has been subjected to pressure and is in reflux, at any point in the cycle the elastic recovery may be determined by relating the difference of friction to the time necessary for the pressure to drain out and equalize the internal pressures, and the thirteenth law of fIiC-r tion may be stated as:

18. At any impressed pressure, the elastic re-v covery of a porous elastic structure in contact with a solid moving body-is the amount of friction reduced per unit of time by seepage flow. I

The capability'of packing of a porous elastic structure to returnto its original state connotes a reflux action, that is, the structure has been temporarily deformed and has stored up some energy which it will return afteran elapse of time. The energy spent in deforming the structure can only be returned thru seepage flow. Thus in Figure 7, the area FoFw is the area of work expended in creating friction due to increase of pressure. The work of causing the packing to react so that this friction is created is called the work of deformation, its exact value being secured from the seepage flow. If suificient time were allowed-for the structure to relax during the reduction of pressure, all of the-work expended on deforming would be returned, less the friction created and the value of the seepage which has found its way to the outside. The area FOFFO' indicates a rapid reduction of pressure, but instead of the stored pressure being returned at its original potential, it is trapped and produces friction, which is a loss. The pressure finally drains out, its volume being related by the hysteresis value FOF, having less pressure potential than the original potential by the amount of friction loss converted to an energy loss. the energy returned by hysteresis action.

Should the structure flux constantly after reduction of pressure frompoint P, as indicated by the dotted friction line F'Ff, the area FoFw represents the work done by the friction created, but

' during the reduction of pressure the friction is less, indicating an apparent gain over the reflux curve B, but actually is aloss of seepage. This will be verified by the seepage flow increase accompanied by a probable leakage of pressure. Thus part of the energy lost in a flux action is due to friction, but a greater amount is increased seepage flow. Comparing flux and reflux reactions, the economical packing will create just as much friction for the rise or fall of pressure, that is, the fluxion value must be unity to secure the most economical operation from any type. Hysteresis is a loss if motion exists before internal pressures are equalized and defluxion is a loss unreplaceable, the former thru friction and the latter from escape of pressure. The minimum loss possible is an equal loss by friction, during the rise and fall of pressure. The capability of a porous elastic structure to return part of the work expended on it is called resilience. The fourteenth and fifteenth laws define the energy necessary to operate a packing:

14. The total work of deformation expended to cause a porous elastic structure to react against a solid moving body is measured by the energy expended thru the flow of seepage.

15. The resilience of a porous elastic structure in contact with a solid moving body is equal to the The area Fo'IDUFo' is potential energy of the seepage returned to the source of energy. I

It seems to be universally accepted that friction is the measure of the power required to'operate a packing, and comparisons are made of similar types on this basis. This is not the fact; as friction is but one manifestation of the energy expended, being the useful work which has resulted from the reaction and contact. The balance of the energy consumed by causing the reaction is larger than the friction created and may be found by measuring the energy represented by the seepage flow. As creating friction to seal pressure is useful work, the friction is needed and desirable. The efficiency of a packing or a porous structure is then:

16. The efliciency of a porous elastic structure in contact with a moving solid body is the. relation ofthe friction to the energy exhausted by the see age flow.

anifestly, it will take so much energy to. seal off an impressed-pressure, and according to the type of the structure, this energy will be manifested. in various forms as losses. To use the friction of contact as a-basis of comparison is erroneous and meaningless, unless the total energy of deformation is also taken into consideration.

Referring now to Figure 8, a fiuxion diagram of starting and stopping the shaft of the machine shown in Figure 1, at regular intervals of time,

increments pa, pa po. The line S is the frictionat start from rest and R is the friction of movement at the same uniform rate, both being due to the rise of pressure. friction at start from rest and R is the friction of movement at the sameuniform rate, both being due to the reduction of pressure. When the packing is installed it is given an initial-set, to form it' around the shaft at pressure m; the friction to set the shaft in motion is F5 which instantly falls to F0 at a. uniform rotation. The shaft is then stopped for m seconds and the pressure advanced to m; the friction starting from rest is point a and falls instantly to b for the same uniform rotation; the shaft is then stopped form seconds and the pressure advanced to m; the friction starting from rest is point 0 and immediately falls to d on rotation. These cycles of repeated stop and start are continued to pressure p, the friction starting from rest being the connected line Fr, which instantly drops to F for the same uniform rotation, the complete series of cycles forming the diverging lines Q and S.

At the pressure p, the shaft is stopped m seconds and 'thepressurereduced to 109; at point r is the friction starting from rest which instantly drops to y for the same uniform motion. The

The line T is the panied change of pressure, such as is common on reciprocating machines and is useful as a method of arriving at the difference of friction for rest and for motion. The friction linesSandQ, of

rest and motion respectively are divergent 'due to the structure endeavoring to occupy a larger volume while seepage continues to flow during the rest periods. During the reduction of pressure, the lines T and R are more widely divergent than those of rising pressure, due to the impedance to flow caused by flux reaction and the changeof position of the rings in the box, which is'still-another matter for examination. Any of the cycles may be solved-for the amount of friction and for location and all of the relations of porosity and density as well as the volume of occupancy may be examined by internal pressures and the rates of seepage flow, using the laws ,before derived.

It has been stated that elastic recovery connotes stored up energy which the structure will return if 'suiiicient time elapses for the pressure to drain away, and that for this to happen, the

structure must be in reflux. It has also been found that if a packing which fluxes during a single impression of pressure, is subjected to "repeated impressions at a rapid rate, that the structure will be in reflux. That is, a Very porous structure will .become saturated with pressure after repeated impressions, if "therate is suf-- ficiently fast; Saturation may therefore occur in two ways: due to the porous structure of the packing and regardless of the length of time of application, and due to-impressionvat a highrate of application. It should also be seen that saturation interferes with the advantages of seepage flow and will reduce the elasticity. Elasticity is desirable, saturation not desirable.

Referring now to Figure 9, the ordinates are of friction and the abcissa of impressed pressure, the fiuxion line U is fro m a porous packing and the curve V is a flux action caused by the reduction of pressure, both for a single impression of pressure. This packing is installed in the machine of Figure'l and the shaft 4 translated for a given strokeat' a high rate of speed. Referring now to Figure 10, representing the saturation diagram of repeated impression of pressure from ro to P at uniform rates of time, the shaft is topped and started at each riseand fall of pressure. measurement and the abcissa are units of time t, the shaft coming to rest at each interval of time. An initial-set friction of F F0 is" given to the packing to coil it around the rod; and the friction from rest is Fr. 'As-the shaft isstarted the friction falls from F, to at the time 53nd then rises again to F1- in the next time interval of ti accompanied by an-increase of pressurefrom zero to P, following theline 21m, and then the shaft .no higher, as'the seepage flow comes to a maximum and prevents an increase offriction. However, if the interval of time is decreased the level F5 will rise, and if increased will fall to the line F0 Fl, for example.

The ordinates are friction to aunit of influx. But due to the rapid impression, the lines zuvwrin Figure are shown in reflux by the friction lines Q and R, of Figure 9, with a hysteresis valueof Fx Po, the same-difference as obtains between the points a: and F0 of Figure 10. .When the level F5 is reached, a cycle is examined along the lines abode; the fiuxion curye T and S of Figure 9 is still in reflux; but there isno hysteresis value for the latter, as the value Fsjis constant.- The hysteresis value of a single imv In Figure'9 the fluxion curve of a singlepressure impression at moderate change is U and V,

\ pression while saturation is increasing becomes a zero value when saturation iscomplete. When I the latter occurs, the result comes under, the heading of saturation due to continued operation.

The two cycles, zuvwa: and abcde, each have points corresponding to the same event in each cycle, are examined by -the internal pr'essure.

charts 10a, 10b, 10c, 10d, and 10e, the ordinates being in impressed pressure andthe abcissa representing the entire length of the packing .set.

On chart 10a; 2' is the internal pressure curve set value F0; c is the residualinternal-pressure at point a' remaining from the previous cycle at point D, from a preceding cycle, showing the effect of saturation. Chart 100 shows point e and v on a common level, the maximum internal pressure curves c, and v coinciding due to the same pressure P, and a common friction value Fr, The shaft stops to reverse its direction and 1 as it startsjthe friction falls, the chart 10d at point a of Figure 10, and is due to the *initialv showing the effect of residual pressure. The

curve to is higher than u of the chart 10b; but curve 02' is the same as b of 'chart 10b: thus the residual pressure begins to cause saturation after.

the first impression at time ti. The chart 10c is the return to the starting point ofthe cycle,

zero pressure, the curve a." being higher than z c of the chart 10a, and e' beingthe same as a of the chart 10a.

- The first sixteen laws of friction as-herein developed are relations ofv pressure andfriction within the confines of the structure and its 'con- The effects of external influences, suchnections. as starting and stopping the shaft and the control of the time element as regards thev reversal of pressures, require further relations which, altho they are based on the first sixteen l ws, are the actual measure of a packing in opera ion. 1,:

Referring again to Figure 10;' ifthe' ,fiuxion values of the packiing are unity, fluxandreflux being in balance, repeated impressions of'pres-' sure would not raise the friction from F0 to F5, but the friction at zero pressure would remain as F0 F0. Perfect elasticity, or instantaneous elastic recovery is desirable and may beapproached bytaking into account the laws which apply to elastic porous structures. "On rotating shafts elastic recovery is not applicable owing to the uniform conditions of rotation and constant pres sure, but does apply if the'pressures are varied.

Therefore all rotating shaft problems should come under the first sixteen laws. The reversal of translation and the wide variation of pressures accompanying, require the relations of elastic reaction and saturation which follow, and should be self-evident: 4 v I 17. For a continued cycle of pressure impressionl. the elutlc reaction of a porom elastic structure in contact with a solid moving body is the ratio of the maximum to the average minimum friction caused 'by the pressure.

18. For a continued cycle. of pressure impressions, the degree of saturation of a porous elastic structure in contact with a solid moving body is the ratio of the increase of the average minimum friction above the initial-set, to the maximum friction.

Nearly all conventional types of packing, braided, platted, moulded and sectional-metallic have been found to obey the eighteen derived laws. One exception has been found. Figure 11 showsa slow-motion fluxion curve of such a. structure which is made of laminated layers of an 1 impregnable material so arranged-that pressure has an immediate ingress and egress to the space between the layers. Starting at an initial-set. of F0, the friction rises approximately proportional to the impressed pressure, as indicated by the line F0 Fn, until the point e is reached. Point e istermed the elastic limit, beyond which the friction is other than proportional to the increase of pressure. During the reduction ofpressure,

the friction rises in an inverse proportion to the point Fr, at zero pressure. On single impressions, the hysteresis value Fr F0v will reduce to F0 after a considerable elapse of time.

In Figure 12, a time-friction. chart, the ordinates are of friction andthe abcissa, of time increments, from 110, t1 .t, and the condition is reciprocation at every time interval with a coincident change of pressure from P to zero,-using a packing such as that used in obtaining the curve shown in Figure,11. Starting at F0, the initialset, thefriction rises to the line F: F5, then drops to the line F0 Fp before the time interval tot1 is complete, .apparen'tly loosing its saturation immediately, or slightly before the reduction of.

pressure. During succeeding impressions of pressure, the maximum and values of friction rise parallel to the lines Fr F; and F0 Fn, then begin to fall to a very low value, and continuing in a low state of friction so long as the shaft is kept in motion.- This exception is given as an example of the stress of deformation which occurs after the elastic limit is passed, yet which will return to. thetoriginal condition, and is to be distinguished from the actual loss of elasticity of the example which follows.

In Figure 13 is shown a fluxion curve of a packing exposed to a pressure too severe for the strength of its structure. Starting at Po, the initial-set, the friction rises proportionally to the pressure up to the point e, the elastic limit, then falls to Fr, and stays at the latter value during the reduction of pressure. The value FrFo is I not hysteresis, but a permanent deformation.

to zero.

' Referring now to Figure 14, a time-friction chart for the packing of Figure 13, gradually approaching permanent deformation, the pressure P is impressed on the structure, at time intervals of to, 1b.. t, and at each interval is reduced At to the friction F6 is the initial-set, and each cycle of pressure events raises the maximum friction to the value Fr. Due to the permanent deformat on occuring and increasing with each cycle, the friction at zero pressure rises on the curved line F0 Fr and coincides with When the coincidence occurs, all reaction of the structure due to pressure ceases and the friction of contact becomes a constant quantity, varying only with the rate of movement.

While the point of elastic. limit is shown in Figures 11 and 13. to mark the reduction of friction as pressure continues to rise, the friction as often rises and increases the coefficient. Therefore at the elastic limit, a decreasing coeflicient denotes a permanent set against the stuffing-box wall,

and an increasing coefficient denotes a permanent set against the rod, or a look as it is frequently L called. From the foregoing relations, the following laws are derived:

19. The elastic limit is reached when the coefficientof elasticity ceases to be a constant value, during the rise of pressure. I l

20. The friction of contact, between a solid moving body and a porous elastic structure, when the latteris subject to the stress of deformation, is proportional to the rise of pressure up to theelastic limit, and beyond the elastic limit is inversely proportional to the rise of impressed pressure, and is consistently proportional inversewith respect to all of the laws derived to prevent confusion, Manifestly, the use of a measured friction related to the impressed pressure would give'erratic results in applying some of the laws. j

There are many friction coefficients to be secured from a single porous structure due to the variations of porosity and the unequal distribution of the applied pressure, this being proven by the first and second laws. The true and the effective values of frictionare therefore defined as:

22. The true coeflicient of friction is the relation of the force. necessary to move a solid'body with respect to an increment of surface of a porous elastic structure, to the normal applied pressure on that surface.

23. The effective coefficient of friction is the relation of the total measured friction to the impressed pressure.-

To further prevent confusion, the definitions.

of pressures as they herein'referred to, are: Inrpressed pressure is the source of pressure to which" the structure is exposed: Internal pressure is the measured gauge pressure at any'point in the structure: The drop of pressure is the impressed pressure less the measured internal pressure at any point; The normal applied pressure is the internal pressure of the structure acting at right angles to the surface'of the solid bodyat any considered point. a

The most important consideration of all of the I relations of friction between an elastic porous structure and a solid body is the distribution of friction as referred to the area of contact, as this relation is the limiting factor of all engineering designs.

An examination of the first and second laws will show that for any impressed pressure there can be any number of mean effective internal pressures, depending upon how the drop of pressure occurs. And it has been stated that the economical relation between pressure and friction is a uniform drop of pressure thruout the structure and away from the source of pressure to secure a uniformly distributed friction per unit of contact area. Based on the latter relation, is the twenty-fourth law:

24. Friction between an elastic porous structure and a solid body is independent "of the surface of contact, when the normal applied pressure The twenty-fourth law is an ideal relation and the sum and substance of all of the minor laws and relations, and is never realized due to the difliculty of distributingthe normal applied pressure, whether the body is confined or unconfined. But it may be closely approximated, as will be shown by succeeding applications for Letters Patent.

The twenty-four laws may be applied mathematically without constants, being the relations of pressure impressed. Variation of speed, change of temperature, the character of the materials in contact, the viscosities of liquids and gases, and the like, are largely empirical, and, while they sometimes vary proportionally to the pressure or other factors, the limits arenarrow and such relations can hardly be called laws. The apparent misunderstanding in designing machinery as to the friction between parts, is a confusion as to what friction is proportional to. It is primarily proportional to the pressure, which when re-v solved into its proper component reactions, will give direct relations which need no constants. As

these laws reflect, the design should be based on the relations to pressure, then allowances made for the simpler factors of speed, temperature and material characteristics.

There are many variations and applications of the laws and relations herein described, but such as may be secured by the method of testing herein described and developed as I shall claim, are construed to be within the spirit of this invention.

I claim: v

The method of testing confined porous elastic packing structures of different 'porosities in contactvwith a solid moving body by impressing a fluid medium under pressure successively against the various packing structures, then simultaneously measuring the internal pressures at the point of contact with said moving body and the friction created by the contact, to obtain the ratio of the change of friction due to the change of internal pressures caused by the variation of the porosity-of the packing with the fluid therein.

HARLEY '1'. WHEELER. 

